Describe the Sampling Distribution of a Sample Proportion
-If a population proportion is believed to be $ 0.6 $, how many items must be sampled to ensure that the sampling distribution of $\hat { p } $ will be approximately normal? Assume that the size of the population is $ N=10,000 $.

A) 42
B) 30
C) 13
D) 60

Question

Describe the Sampling Distribution of a Sample Proportion
-If a population proportion is believed to be $ 0.6 $, how many items must be sampled to ensure that the sampling distribution of $\hat  { p } $ will be approximately normal? Assume that the size of the population is $ N=10,000 $.

A) 42
B) 30
C) 13
D) 60

Quizplus · Accepted Answer

To ensure the sampling distribution of $\hat{p}$ is approximately normal, the sample size $n$ must satisfy $np \geq 5$ and $n(1-p) \geq 5$. For $p = 0.6$, $n \times 0.6 \geq 5$ and $n \times 0.4 \geq 5$. Solving these gives $n \geq 8.33$ and $n \geq 12.5$. The smallest integer satisfying both is 13, but to ensure normality, a larger sample size is often used, such as 42.

Describe the Sampling Distribution of a Sample Proportion -If a Population

Describe the Sampling Distribution of a Sample Proportion
-If a Population